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The readout MR signal is stored in K-space which is equivalent to a Fourier plane. To go from a k-space data to an image requires using a 2D inverse Fourier Transform. The k-space location (kx and ky coordinates) of data is governed by the accumulated effect of gradient events and excitation pulses

The readout MR signal is stored in K-space which is equivalent to a Fourier plane. To go from a k-space data to an image requires using a 2D inverse Fourier Transform.

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Frequency-encoding and phase-encoding are done so that data is spatially encoded by differences in frequency and phase, amenable to analysis by Fourier transform. In k-space, fx-coordinates (horizontal spatial frequencies) and fy-coordinates (vertical spatial frequencies) of the Fourier plane are replaced by kx and ky-coordinates.

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A classic spin echo sequence fills the k-space line by line. Here is the explanation of the k-space trajectory :

Repetition for each line with increasing phase-encoding gradient strength (negative to positive intensity). The amount of gradient phase change between adjacent line is constant. This results in a sequential (line by line) filling of k-space from top to bottom.

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The k-space location (kx and ky coordinates) of data is governed by the accumulated effect of gradient events and excitation pulses. Here are the rules for moving in k-space:

The initial RF excitation pulse (with the slice-selection gradient) is the beginning of the sequence: location is at the center of k-space.

A 180° RF pulse causes a jump to the opposite location.

The greater the net strength of the phase-encoding gradient (or the longer the gradient is on), the farther from the k-space origin the data belong, in the upper direction if the gradient is positive or in the lower direction if the gradient is negative. As the duration of phase-encoding gradient is most often constant, the strength of the phase-encoding gradient governs the location on the vertical axis (ky-coordinate).

The longer the frequency-encoding gradient is on (or the greater the net strength of the gradient is), the farther from the k-space origin the data belong, in the right direction if the gradient is positive or in the left direction if the gradient is negative. As the strength of the frequency-encoding gradient is most often constant, the duration of the frequency-encoding gradient governs the location on the horizontal axis (kx-coordinate)

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